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DI'1'ItODUC'1'::tOll The assumption of treating the catamaran resistance of as a

summation in order resistance

of a number to and Such

of independent

components

can be made catamaran on the

facilitate

understanding of hull allows one

the influence a division better

separation

resistance. but also purpose, methods a

not only to carry purposes for

out systematic

model experiments scaling of the review

for comparative available

to provide brief vessels

to full scale. For this methods of these

conventional

is made, resistance in

and modifications are suggested. hull

for catamaran used

The methods dividing measurement formulae, method. or

conventional

testing

by the with Both

resistance of

into components frictional

are based on either from

of total resistance direct measurements considered involved of

from model experiments resistance of the components.

the estimation are

empirical

in order to identify

the components

and the assumptions The separation consideration a tank pattern

in such a division. into components from

resistance to obtain

of the momentum

principle

for a ship model in for wave

is formulated

the expressions

and wake traverse

resistance. between components the demihulls in which

The interference modify the configurations

effects

resistance are described.

catamaran

known as the total resistance. such as Froude's. two main methods are in common use by experimental tanks: i) By measuring total resistance and employing an empirical formula for frictional resistance.possible to present these components in a diagrammatic breakdown as shown in Fig. This allows one not only to conduct the experiments on scaled models for the prediction of resistance of the full scale ship. but also to carry out systematical model experiments to optimise a particular resistance characteristic of a hull form. ITTC-1978 and direct measurement methods for the determination of catamaran resistance are introduced by defining interference factors.2 RBSIS~ARCB COMPORBRTS OF A SHIP MODEL A ship model.
3.28 Modified ITTC-1957. It is. Although these methods have not yet been proven. This total resistance can be split into a number of components. or Hughes' Methods.72]. they may be assumed to be independent of each other for practical purposes. [12. A practical method for the determination of the components can be established. in such a way that it opposes its motion and acts parallel to the motion of the model.
.39. Discussions on the justification of such a division of resistance into components and on the interdependence of these components can be found in Refs. Although these components interact with each other in a very complicated way. Although several methods can be deduced from this figure for use in a towing tank.
.69. 29. it is considered that such an approach would provide a better understanding of the components and interference effects. moving on the undisturbed free surface of a fluid with a constant speed experiences a force.

(RRM/~)=(RRs/~) for corresponding speeds which can be obtained from (VH/lgLM)=(Vs/lgLs) for which the wave patterns of model and ship are similar. as it is fairly easy to measure the total resistance.
(3.3. However the division into components is hypothetical.e.
w.3 BSTIMATION The of skin
OF RBSISTANCB
COMPONBNTS
methods
resistance from
the measurement of total towing tank experiments and the estimation by an empirical formula are
based
on
friction resistance
very practical for extrapolating the model results to ship scale.29 ii) By measuring the components directly a laborious using advanced but physically
experimental
techniques.1) Furthermore. RTM = RFH + RRH where RTM= Total resistance of model measured from experiments RFM= Frictiona~ resistance for a flat surface having the same wetted surface as the model which can be obtained from RFM = f S VB f.1 FROUDB'S APPROACH Froude was the first person to present a breakdown of total resistance into components [20.21]. i.
justifiable method can be achieved.
3.
3. Froude assumed that residuary resistance of a model is correlated to the ship by the ratios of the displacements.n Constants which are functions of length and nature of the surface RRM= Residuary resistance of model calculated from (3.1)
.

series of experiments with
planks were conducted by several researchers resulting in improved friction resistance formulations for flat surfaces among which the following are the most used ones [28]: ATTC .3.5)
It must be emphasised that all these methods are based solely on Froude's assumption that total resistance is the summation of the frictional resistance calculated from formula and residuary resistance obtained from experiments.2)
3.4)
these formulations and in 1957 suggested
a new formula for skin friction "ITTC 1957 model-ship correlation line "and implying this line was only an interim solution to the problem for practical purposes. results can be extrapolated to by using a resistance coefficient presentation ship
(3.3)
HUGHES 0.242
=
log(Re CF) (3. wave breaking. spray. ITTC 1957 0.067 (log(Re)-2. In this assumption scale effects for surface tension. and form effect on the frictional
.03)2 ITTC studied (3.30 Using Froude's method.2 IMPROVBMBNTS
ON FROUDB'S
APPROACH
Following Froude's
method.SCHOENHERR 0.075 CF = (log(Re)-2)2
(3.

3. wave resistance.35] proposed a method for use in model ship correlation which regards total resistance as a sum of three components i) Frictional resistance as the resistance of a plane surface of the same area and the same length as model. Hughes assumed that for a streamlined body in turbulent flow it can be expressed as a proportion of the frictional resistance. ii) Form resistance as the excess over item (i) in the case of the deeply submerged body. In this method total resistance for a ship is divided into four components:
. the 15tb ITTC Resistance committee proposed a
new method called " 1978 ITTC Performance Prediction Method for Single Screw Ships " [41].e. Hence C. iii) The excess of summation free surface of the resistance. R. (Re
=
VL
v
.e.7)
(l+k) is called the form factor and can be found from very low speed experiments where Cw can be neglected. i.3 FORM FACTOR MBTBODS
In 1954. is the for the surface model from the resistance and the form
total resistance
frictional
resistance of the model.
=
=
CF + CFO + Cw (l+k) CF + Cw
where CFO
=
k CF (3.
Fn
= ---) =
rgL
V
RF (Re) + RR (Fn)
(3.6)
3. The interactions between the viscous and gravitational forces are not taken into account. C. i. In 1978. Hughes [34.31 resistance are neglected.

2) CT = (l+k) CF + a FnD
(3. In practice low speed experiments are often not accurate enough due to instrumentation inaccuracy.4 DIRECT MEASUREMENT OF RESISTANCE COMPONENTS
of physically identifiable A number resistance components can be measured directly from towing tank experiments by utilising advanced experimental techniques. ACF CAA = Frictional resistance from ITTC-1957 Line = Residuary resistance from model experiments = Roughness allowance (0 for a smooth model) = Air resistance (assumed 0 for a model without superstructures)
The recommended method to find k is by low speed measurements where c.a. There are two well known methods in use :
.n can be solved from a least squares analysis of low speed measurements.8)
where (l+k) = form factor CF C. transom stern vortices and bilge vortices may occur.
3.32
CT = (l+k) CF +
c. hence scaling between the model and ship can be done more accurately. In the form factor methods.
+ ACF + CAA
(3. In the case of models where flow separation. But (l+k) is assumed to be independent of speed. Reynolds number effects on the form factor may have to be considered. Therefore another method due to Prohaska is recommended: Assuming CRM = a FnD for low speeds (generally Fn<0. form effect on frictional
resistance is taken into account.9)
(l+k). approximates to zero and (l+k)=CT/CF. hence Reynolds number and Froude number.

g.30) in a as given in as:
from considerations
1B
B. Wave pattern time needed. PeeII:tE
G. surface.
measurements and pressure pressures and to be on very
of tangential resistance the hull
hull surface
derived
surface. from the of can be interpreted the skin as a summation stresses of on
namely
friction
resistance from the i. of momentum
1B
(u'
Derivation
these components Appendix
W/2
may be made for a ship model changes
(Fig. see Ref.e. for
ii) Alternatively. 'lb.09
Oistrihttim of SOn Ftict:im m a M:xEl.2 Ftict::imal cn:i PtessJre ~ 1967 ti:1. from
as the summation
of wave pattern measured i.e. requires up induced
= CwP + CWT
The assumption
drag is acceptable
most conventional This method derive the experimental Experimental analysis set
more sophisticated than the and first quicker
techniques one. whilst
is now used extensively
the wake traverse
is less preferred This resistance tank method
due to the long experimental is chosen in for
direct measurements
components
the current work.B. but
to the
components errors
is easier
to conduct. This leads to representation
W/2
of resistance
Rt=
JJ
-H
AP dzdy + 1/2
JJ
-H
-u') dzdy
-W/2
-W/2
)I:
'1tHBin R. CT
resistance
wake traverse
resistance
in the wake of the model.N. of negligible craft. steele B.L. energy derived viscous head loss approach from the
total resistance energy loss in
can be deduced created waves. from an and the the total .
69. of the of
are also less pronounced. to
This method laborious have
is relatively
straightforward
sensitive
measurement of relatively whole hull
since
the shear stress
and pressures
magnitude
measured
over the
It is therefore
not commonly
used in practice. ~
~
c1 tiE
AEtltx:n" G:arlJrs 'lRlH\
. also small very errors.33 i) the the Total resistance forces acting. but is
obtained measurement CT=Cy+CP*. of a Hidl &arl LiIe:' 'lRlH\ 1968 ti:1l0 cn:i
of 'Do''I1q
e.

w y_.10) from wave of the are
velocity in the The
loss case The first represents wake resistance model wave determined theory.!!.
due to the influence
of other demihull.
due to
the hulls. The interaction
can be divided
into two distinct
1) Body interference is asymmetric
: The flow around
a symmetric
demihull i.5 RESISTANCE
COMPOHBHTS
OF A CATAMARAN of a catamaran present much
The resistance more complicated the interference effects
components than between
phenomena effects
those of monohulls groups.e.
velocity is the
components by utilising drag. y. The first two traverse which from it can line equation is the y_. v.'
18
W/2
dy + 1/2
JJ
18
(Y'+~'-Y') dzdy
-W/2 W/2
-W/2 -H
+ 1/ 2
J J [(
v' -v')
+ (w' -w')
-
(u'
-!!' ) 1 dzdy
(3. can be The
pattern.
this wave pattern not be
linear wave
third line
induced
easily measured
unless
3.
. Unlike all the viscous resistance defined can be derived line an analysis
surveys.y. 18 llP
U
perturbation wave orbital wave height fictitious
velocities velocities at B
at B at B
![
head loss between
A and B at B corresponding resistance which from second to no head (3.34 W/2
+ Ig/2
J 1.10)
-W/2 -H where u.

. In these experiments the cross flow velocity in the y direction is about 5-7 % of the model speed. e) As the waves of one demihull reach the other hull. d) The velocity increase on the tunnel side may change the structure of the boundary layer. c) Because the wave heights at the stern inside and 10 % in the x the demihull in The perturbation velocity
outside o~ the demihull are different. tunnel side. Crossflow in the entrance is outwards. especially on the inside. This causes vortices and spray at the stern resulting in an induced drag component. of the hull due to the venturi effect. b) A cross flow may occur under the keel which can lead into an induced drag component which is normally neglected in monohulls. This has following outcomes: a) around the demihull increases. the wetted surface. This velocity augmentation causes an increase in skin friction resistance and modifies the form factor. Experiments of Miyazawa [51] and Schimke [68] indicate an increase in perturbation velocity of up to direction compared with that of isolation. Miyazawa [51] has suggested that this component is relatively small compared with (a) in his experimental results. and therefore the skin friction resistance. while in the run it is inwards.35
the
pressure
field
is
not
symmetric
relative
to
the
centreline of the demihulls. the flow at the stern can show inwards or outwards flow. can change. Although this component is reported to be important in symmetric catamarans by Pien [60].

e) Inward or outward flow at the stern changes the
wave formation Taking methods for catamarans the
at the stern. can become even in breaking
bow waves of the other demihull superposition resulting in an unstable wave. field.11)
where
. the for
interference :
monohulls as follows
described
can be adapted
ITTC 1957 Method (CT)CAT
= =
(CF)CAT + (Ca)CAT a CF
+
Q
Ca
(3. The transverse reinforced by the other of the other
a demihull divergent by
wave of the one hull can be stern wave of the same bow wave from
the divergent reflection
by the
the other hull. c) The demihull d) The reflections complicate of divergent waves from the other
the interference
phenomena.36
2) Wave side by
interference:
As a
result effects
of
two hulls running may
side. interaction between
favourable of the
unfavourable demihulls bow is always
the waves wave of cancelled hull or hull while
may occur. effects earlier into account. the and
bow wave of a demihull of
in the tunnel meets on the centerline. wavemaking the wave than from the
In other words
of a demihull
may be different
case of the demihull or
in isolation. interference
on wave resistance
also be observed.
these two waves
very high waves
and spray at high speeds. a) Due to the change of the assumed b) A demihulls may formation in the pressure change.

)CAT + (Cw)CAT (1+_ k ) a C. The residuary resistance interference factor Q can be investigated from experimental results. ITTC 1978 Method (CT)CAT
= ( 1+kcAT)
=
(C.12) as in ITTC
where a Frictional resistance interference factor 1957 method.55 and 78. The tendency of this factor due to variation of separation and speed is given in Refs.37
a
Q
Frictional resistance interference factor
Residuary resistance interference factor subscript CAT denotes catamaran
The velocity augmentation between the hulls may be taken into account by introducing an interference factor a which would be calculated from the integration of local frictional resistance over the wetted surface. It is mainly dependent on the separation. due to cross flow. For practical .)
.(Cw )CAT + (Cwp ) CAT + (CI) T CAT = « CWT + p CwP + (CI)CAT where « Wake traverse interference factor p Wave pattern resistance interference factor
(3. vortices etc. _ and
interference factor ~ where (l+_k) a = (l+~k). The wave resistance interference factor can be determined from experimental results.. Direct Measurement Method
change around a demihu11.13)
CI: Coefficient of induced drag (e.0 can be combined into a viscous resistance
(CT)CAT .g. _ Form resistance interference factor ~ Wave resistance interference factor _ is introduced to take into account the effects of
pressure field purposes.. + ~ Cw
(3.

without any
where
Cr =
ii)
The ITTC 1978
correction
for surface
roughness
For Monohulls CT = Cv + Cw : = (l+k) Cr + Cw For Catamarans (CT)CAT= where Cr (1+ ~k) Cr + ~ Cw is calculated from the ITTC 1957 Model ship
correlation
line.
data are sparse.38
The wake traverse wave breaking Miyazawa differs may suggested from ~ and
interference «can
factor. case due
(CI)CAT to cross
be of importance
in the
catamaran
flow.
3. directly p from
interference that
Q as
as well as viscous be taken as defined it can be Although
wave pattern
experiments. three main methods components
are utilised of catamarans i) The
in order to explore in the current work was
the resistance
ITTC 1957 approach
used as the simplest
method
of separating For Monohulls CT = Cr + CR For Catamarans
the resistance
into components
(CT)CAT= a Cr + Q CR 0.6 SUMMARY From the methods described above. (l+(B/S)2).075 (Log(Re)-2)2 method for the ship model or air drag. will include interference. induced vortices
and spray.
.
«.